This study will determine if raloxifene is either more or less effective than tamoxifen in reducing the incidence of invasive breast cancer in postmenopausal women who are at increased risk for the disease. A secondary goal is to determine whether raloxifene reduces the endometrial cancer rate compared to tamoxifen. Approximately 22,000 postmenopausal women 35 years of age or older who are at increased risk for the development of breast cancer will be randomly assigned in this double -blind trial to receive daily either 20mg of tamoxifen plus a placebo or 60mg of raloxifene plus a placebo, for a period of 5 years. Women will be eligible for this trial if they are postmenopausal and their projected 5-year probability of developing invasive breast cancer is at least 1.66%, or if they are postmenopausal and they have a history of lobular carcinoma in situ (LCIS).